A Higher-order Block Method for Numerical Approximation of Third-order Boundary Value Problems in ODEs

In recent times, numerical approximation of 3rd-order boundary value problems (BVPs) has attracted great attention due to its wide applications in solving arising from sciences and engineering. Hence, A higher-order block method is constructed for the direct solution linear non-linear BVPs. The approach interpolation collocation adopted derivation. Power series approximate interpolated at points required suitably handle both third-order BVPs while was done all multiderivative points. three sets discrete schemes together with their first, second derivatives formed (HBM) which applied standard HBM self-starting since it doesn’t need any separate predictor or starting values. investigation convergence analysis completely examined discussed. improving tactics are fully considered discussed resulted better performance HBM. Three examples were presented show strength over other methods. comparison errors existing work literature also shown curves.